1. Olivia finds a combination of two different transformations that moves ABCDE onto A"B"C"D"E". What is one way she might have done this? (3 points)
2. Angelica reflects ABCDE over the y-axis and translates it up 8 units. Does her transformed figure match A"B"C"D"E"? If not, describe how her transformed figure compares to A"B"C"D"E". (3 points)
3. Michael says he can move ABCDE onto A"B"C"D"E" with one transformation by translating ABCDE diagonally so that it moves 8 units up and 10 units right. Is he correct? Explain why or why not. (4 points)
Answers
Using the graphs, Olivia is correct if she used one of those two approaches. Michael and Angelica both use the wrong strategies.
What are graphs?An organised-representation of the data is all that the graph is. It facilitates our understanding of the facts. Data is the term used to describe the numerical information obtained through observation.
The development of a research question is followed by the ongoing observational collection of data. The data is then organised, distilled, categorises, and visually represented.
Information and data have different purposes: Data is an unadorned truth; information is the meaning that can be inferred from data.
Challenge 1
Olivia may have, for example, translated 10 units to the right after reflecting over the x axis.
Let's use point C to apply this series of steps.
C = (-2,-4) (-2,-4)
After reversing the x axis, C' becomes (-2,4); the y coordinate changes sign, and C" becomes (8,4) after moving to the right by 10 units. The x coordinate is then increased by 10.
The graphic shows that point C (-2, -4) shifts to C"(8,4). The other four points I'll let you investigate.
Olivia may have also tried shifting 10 units to the right before reflecting across the x axis. The sequence here is irrelevant. Order does important, though, for several other combinations of transformations.
Challenge 2
The point (x,y) will become after reflection across the y axis (-x,y). Here, the sign is reversed, and only the x coordinate changes. The y coordinate remains constant.
With the y axis reflection, a point like C (-2, -4) becomes C'(2, -4). By moving up 8 units, we get at C"(2,4) by adding 8 to the y coordinate, but this is not what the graphic displays. Thus, Angelica's approach is flawed.
The last four points should also contain other contradictions, as well.
Challenge 3
Even Michael's approach is flawed. Instead of using an x axis reflection, he completely relies on translations to change ABCDE into A"B"C"D"E".
Quick inspection suggests that Michael might be right. Yet, if you examine much more closely, you'll notice that things aren't exactly in line.
This time, we'll choose point D rather than point C.
D can be found at (-6, -2). To reach D' if we move up 8 units, we must add 8 to the y coordinate (-6,6). Then, to move 10 units to the right, add 10 to the x coordinate. And brings us to D" (4,6).
The diagram, however, reveals that D" is actually at (4,2)
Let you examine the other points, please. The only points that should go to the right places are C and E; the remaining points should not. Once more, Michael's failure to apply an x axis reflection is to blame. His A"B"C"D"E" figure is reversed from how it should have been.
To sum up, the strategies mentioned in problem 1 are the proper ones to use in order to make ABCDE go to A"B"C"D"E. Olivia is correct if she used one of those two approaches. Michael and Angelica both use the wrong strategies.
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Related Questions
common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and 95th percentile for men . In designing a work table the sitting knee height must be considered. Males have sitting knee heights that are normally distributed with a mean of 21.3 and s/d 1.2, Females have a mean of 19.9 in and a s/d of 1.1 . what is the minimum clearance required for safety of fitting 95% of men . True or False if 95% clearance for males ,there will certainly be clearance for all 5% of women. does the table fit anyone , what percentage. What percentage of womenfit the table.
Answers
The minimum clearance required for safety of fitting 95% of men is approximately 18.7 inches.
What is percentage ?
Percentage is a way of expressing a proportion or a ratio as a fraction of 100. It is often represented by the symbol % and is used to compare values, make comparisons, and analyze data. For example, if there are 25 red marbles and 75 green marbles in a jar, the percentage of red marbles is 25% (25/100), while the percentage of green marbles is 75% (75/100). Percentages are commonly used in many fields, including finance, business, statistics, and science.
To determine the minimum clearance required for safety of fitting 95% of men, we need to find the value of the sitting knee height at the 95th percentile for men.
Using the formula for a normal distribution, we can calculate that the sitting knee height at the 95th percentile for men is approximately 23.2 inches.
Therefore, the minimum clearance required for safety of fitting 95% of men would be the difference between the sitting knee height at the 95th percentile for men (23.2 inches) and the height of the work table.
Therefore, the minimum clearance required for safety of fitting 95% of men is approximately 18.7 inches.
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Please need help 15 points !!!
Which describes the correct order of steps for constructing an angle bisector
of ZDEF using only a straightedge and compass?
A. 1. Draw a circle with a radius less than DE and center E, and label
the points of intersection G and H.
2. Draw a circle with radius GH and center G and another circle
with radius GH and center H, and then draw an equilateral triangle.
3. Use a straightedge to connect E to the rightmost vertex of the
equilateral triangle.
4. Draw a line from point G to point H.
B. An angle bisector cannot be constructed using only a straightedge
and compass.
C. 1. Draw a circle with a radius less than DE and center E, and label
the points of intersection G and H.
2. Draw a line from point G to point H.
3. Draw a circle with radius GH and center G and another circle
with radius GH and center H, and then draw an equilateral triangle.
4. Use a straightedge to connect Eto the rightmost vertex of the
equilateral triangle.
D. 1. Use a straightedge to connect E to the rightmost vertex of the
equilateral triangle.
2. Draw a circle with a radius less than DE and center E, and label
the points of intersection G and H.
3. Draw a line from G to H.
4. Draw a circle with radius GH and center G and another circle
with radius GH and center H, and then draw an equilateral triangle.
Answers
Correct order of steps for constructing an angle bisector of ∠DEF using only a straightedge and compass is option C.
What is angle bisector?A angle bisector is a line that bisects an angle into two equal angles. A bisector means dividing a shape or object into two equal parts. When we draw a ray that bisects an angle into two equal parts of equal magnitude, it is called a bisector.
Given,
Compass and straightedge to draw angle bisector of ∠DEF
Steps to draw angle bisector are:
1. Draw a circle with a radius less than DE and center E, and label
the points of intersection G and H.
2. Draw a line from point G to point H.
3. Draw a circle with radius GH and center G and another circle
with radius GH and center H, and then draw an equilateral triangle.
4. Use a straightedge to connect E to the rightmost vertex of the
equilateral triangle.
Hence, option C describes correct order of constructing an angle bisector of ∠DEF using only a straightedge and compass.
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Marie made a scale drawing of a boarding school. She used the scale 6 millimeters = 8 meters. What scale factor does the drawing use?
Simplify your answer and write it as a fraction.
Answers
Therefore, the scale factor used in the drawing is 4000/3.
What is factor?In mathematics, a factor refers to a number or algebraic expression that divides another number or expression without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because each of these numbers can be multiplied by another whole number to produce 12 (1 × 12, 2 × 6, 3 × 4). Factors play an important role in many areas of mathematics, including algebra, number theory, and geometry, and are used to simplify expressions, solve equations, and factorize polynomials.
Given by the question.
The scale factor is the ratio of the length of an object on the drawing to the actual length of the object.
Since 6 millimeters on the drawing represents 8 meters in reality, the scale factor can be expressed as:
Scale factor = Actual length / Length on drawing
Scale factor = 8 meters / (6 millimeters)
To simplify this fraction, we need to convert meters to millimeters by multiplying by 1000:
Scale factor = (8 meters * 1000) / 6 millimeters
Scale factor = 8000 / 6
The fraction cannot be simplified further, so the scale factor is:
Scale factor = 4000/3
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what is P(less than 3)
Answers
Answer:-3p
Step-by-step explanation: less = subtract -3+p=-3p
how to find the inverse for question B. Y = 4x^2-2
Answers
Answer:
x = ± √((y + 2)/4)
Step-by-step explanation:
To find the inverse of a function, we need to solve for x in terms of y.
Steps to find the inverse of y = 4x^2 - 2:
Replace y with x and x with y:
x = 4y^2 - 2
Solve for y:
x + 2 = 4y^2
(x + 2)/4 = y^2
± √((x + 2)/4) = y
Note that we have a ± sign because the square root of a positive number can have two values, one positive and one negative.
Therefore, the inverse of y = 4x^2 - 2 is:
x = ± √((y + 2)/4)
Answer:
y=±([tex]\sqrt{x+2}/2[/tex])
Step-by-step explanation:
Calculate the value of the expression-6(-5-4)-4(-3-2)=
Answers
Answer:
74
Step-by-step explanation:
-6 (-5 - 4) - 4(-3 - 2)
30 + 24 + 12 + 8 = 74
Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each
section of Finite Math has 40 students and earns the college $40,000 in revenue. Each section of Applied Calculus has 40
students and earns the college $60,000, while each section of Computer Methods has 10 students and earns the college
$29,000. Assuming the college wishes to offer a total of seven sections, accommodate 220 students, and bring in $298,000
in revenues, how many sections of each course should it offer?
Finite Math
Applied Calculus
Computer Methods
Need Help?
Read It
section(s)
section(s)
section(s)
Watch It
Answers
Answer:
Step-by-step explanation:
Let's use the following variables:
Let F be the number of sections of Finite Math
Let A be the number of sections of Applied Calculus
Let C be the number of sections of Computer Methods
We can create a system of equations based on the given information:
F + A + C = 7 (the college wishes to offer a total of seven sections)
40F + 60A + 290C = 298000 (the college wishes to bring in $298,000 in revenues)
40F + 40A + 10C = 220 (the college wishes to accommodate 220 students)
We can solve this system of equations using any method we prefer. Here's one possible way:
Multiply the third equation by 10 to get:
400F + 400A + 100C = 2200
Subtract the third equation from the second equation to eliminate C:
20A + 280C = 76000
Multiply the first equation by 40 and subtract it from the previous equation to eliminate A:
240C = 76000 - 1600
Solve for C:
C = 290
Substitute C = 290 into the third equation to solve for F:
40F + 40A + 10(290) = 220
40F + 40A = -2680
F + A = -67
Substitute C = 290 and F + A = -67 into the first equation to solve for A:
A = 10
Substitute A = 10 and C = 290 into the first equation to solve for F:
F = -3
We have a problem here: we obtained a negative number of sections for Finite Math, which is impossible. This means that the original system of equations is inconsistent, and there is no solution that satisfies all the requirements.
Therefore, the college cannot offer the desired number of sections while accommodating the desired number of students and revenue. Some adjustments need to be made, such as changing the number of students per section or the tuition fees.
You visit six randomly selected locations on campus and observe the number of people in the area using their cell phone. The data is as follows: 3, 4, 4, 5, 6, 8 1.
1. What scale of measurement was used by the researcher?
2. Calculate the mean, median, mode for the data set.
3. Calculate the range, variance and standard deviation for the data set (use the formula for sample).
4. Based on the sample, what is the number of people using their cell phone associated with +1 SD?
5. What number of people using their cell phone reflects 96% of the sample?
Answers
Answer:
The researcher used a ratio scale of measurement for the number of people using their cell phone.
Mean: (3+4+4+5+6+8)/6 = 30/6 = 5
Median: arrange the data in ascending order: 3, 4, 4, 5, 6, 8. The median is the middle value which is 5.
Mode: there is no mode as no value occurs more than once.
Range: 8-3 = 5
Variance:
s^2 = Σ(x-ȳ)^2 / (n-1)
s^2 = [(3-5)^2 + (4-5)^2 + (4-5)^2 + (5-5)^2 + (6-5)^2 + (8-5)^2] / (6-1)
s^2 = 5.6
Standard deviation: s = sqrt(s^2) = sqrt(5.6) ≈ 2.37
To find the number of people using their cell phone associated with +1 SD, we add one standard deviation to the mean:
Mean + 1 SD = 5 + 2.37 ≈ 7.37
Therefore, approximately 7 people using their cell phone are associated with +1 SD.
To find the number of people using their cell phone that reflects 96% of the sample, we need to find the z-score that corresponds to the 96th percentile. From a standard normal distribution table, we find that the z-score is approximately 1.75. We can use this z-score to find the corresponding value in our data set using the formula:
z = (x - ȳ) / s
Rearranging, we get:
x = z * s + ȳ
x = 1.75 * 2.37 + 5
x ≈ 9.3
Therefore, approximately 9 people using their cell phone reflect 96% of the sample.
Step-by-step explanation:
200 904/1000 as decimal
Answers
Answer:
200.904
Step-by-step explanation:
200904 is the same as 200904.0
On dividing by 1000, the point moves three steps to the left, 20090.4 , 2009.04 then finally 200.904.
What is the area of the drawing of the sailboat in square centimeters??
Answers
Answer:
Step-by-step explanation:
triangle-
b+h/2=a
5x6/2=30
rectangle-
2.5x12=30
area of drawing-
30+30=60
answer:60cm^2
What equation can be used to find the circumference of the circle below
Answers
Answer:
C = 2 x 4.5 x π
Step-by-step explanation:
The equation to find the circumference of the circle is
C = 2π · r
r = 4.5 in
Looking at the options, the answer is C = 2 x 4.5 x π
Answer:
Below
Step-by-step explanation:
radius = 4.5 diameter = 2 x 4.5 in
the circumference of a circle is given by the formula p * d
substitute in the underlined equation for 'diameter')
circumference = 2 * 4.5 * pi inches
The measures of the angles of a triangle are in the ratio 1:9:26. What is the measure of each angle?
Answers
The angles of the triangle will be 5 °, 45 °, and 130 °.
How do triangles function?The triangle is a two-dimensional geometric object with three straight sides and three angles. The lengths of the triangle's three sides can differ from the third side (isosceles triangle), be equal (equilateral triangle), or be any combination of the three (scalene triangle).
The sum of the angles in a triangle is always 180 degrees; the opposite angle of the longest side is the largest, and the opposite angle of the shortest side is the smallest.
Now,
Let x be the common factor that multiplies the ratio of 1:9:26. Then, the measures of the angles can be expressed as x, 9x, and 26x.
Since the sum of the angles in a triangle is always 180 degrees, we can set up an equation:
x + 9x + 26x = 180°
Simplifying the equation, we get:
36x = 180
Dividing both sides by 36, we get:
x = 5
Therefore, the measures of the angles are:
x = 5 degrees (the smallest angle)
9x = 45 degrees
26x = 130 degrees (the largest angle)
So the angles of the triangle are 5 degrees, 45 degrees, and 130 degrees.
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A 27-meter rope is cut into two pieces so that one piece is 2 meters longer than 4 times the shorter piece. Find the lengths of both pieces.
Answers
27-2=25
25:5=5
4(5)+2=20+2=22
the shorter piece = 5
the longer piece = 22
Explain why m/NMO = 20°
Answers
Because of the isosceles triangle.
What is the isosceles triangle?The triangle whose two sides are equal length is called an isosceles triangle. The third side, known as the base, may or may not be a different length from the other two sides. An isosceles triangle also has two angles that are equal in measure, which are opposite the two equal sides.
Given that in ΔMQN: MQ=MN,
therefore, ∠MQP=60°=∠MNO (isosceles triangle )
also given in ΔMPO: MP=MO,
therefore, ∠MPO=80°=∠MOP (isosceles triangle )
For the straight line PON,
∠POM + ∠MON = 180° (straight line angle)
80° + ∠MON = 180°
∠MON = 100°
In ΔNMO,
∠NMO +∠MON + ∠MNO = 180° ()
∠NMO + 100° + 60° = 180°
∠NMO = 20°
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PLEASE HELP QUICKLY ITS DUE BY TOMORROW
Answers
The total area is given as 160 sq feet. The total yard that is to be purchased is 18 yards
How to solve for the area of the roomTo get the area of the room we would first have to find the area of the sides.
We can call 1 of the areas S1.
The length l1 = 13
The width w1 = 16
area =
s1 = 13 * 16
We have
s2 with
l2 = 6
w2 = 8
then the area
s2 = 6 * 8
S1 - s2
= 208 - 48 =
160
1 square yard = 9 square foot
17.7778 = 160 square feet
Juan has to purchase approximately 18 yards
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Uber charges a $10 pickup fee and $0.10 per mile driven Lyft charges a $5 pickup fee and $0.25 per mile driven How many miles will need to be driven for the companies to be the exact same price?
Answers
Answer:
The two ride-sharing companies will have the same price after 40 miles have been driven. At that point, both companies will have charged $10 in pickup fees and $10 in total for miles driven, meaning the cost of taking either service will be the same
Step-by-step explanation:
which is th product of 5 x 2 1/3 A. 11 2/3 B.4 2/3 C.35 1/3 D. 3 1/3 Which answer is correct
Answers
the product will be 35/3.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
product of 5 x 2 1/3
=5*7/3
=35/3
Hence the product will be 35/3.
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oranges are being sold for $ 1.25 per pound. use this rate to complete the equation where c is the total cost of wpounds of oranges do not include units or a dollar sign.
Answers
The equation would be C = 1.25w, where c is the total cost of w pounds of oranges do not include units or a dollar sign.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
The unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit.
We are given that oranges are being sold for $ 1.25 per pound.
The equation would be as;
C = 1.25w
where c is the total cost of w pounds of oranges and does not include units or a dollar sign.
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Solve the system of equations below graphically. Identify the graphs and the solution point on the Cartesian plane below.
x-y=0
5x+2y=7
Answers
A solution to the given system of linear equations is (2, 6).
How to graphically solve this system of equations?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
x - y = 0 ......equation 1.
5x + 2y = 7 ......equation 2.
In this exercise, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.
Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (1, 1).
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pls help me with the algebra assignment
Answers
Answer:333
Step-by-step explanation:53533535
Which of the following theorems verifies that ABC-DEF?
AA
63°
63
C
D
OA: AA
OB. HA
OC. LL
D. HL
Answers
The theorem that justifies the similarity of the two triangles is given as follows:
A: AA.
What is the Angle-Angle Similarity Theorem?The Angle-Angle (AA) Congruence Theorem states that if two pairs of corresponding angles are congruent, then the triangles are similar.
In other words, if two angles of one triangle are equal in measure to two angles of another triangle, then the third angle in each triangle must also be equal in measure, and the two triangles are therefore congruent.
The two pairs of corresponding angles that are congruent in this problem are given as follows:
63º and 63º.90º and 90º. -> right angle.Hence the third angle will also have the same measure for both triangles.
Hence the AA theorem can be used and the correct option is given by option A.
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In the figure, a || e,m || n, and m<2 =112
What is the m<6?
Answers
Answer:
look in the comments give me a minute please and thank you
a girl is paid $840 for a basic fortnight of 25 hours . calculate her basic rate.
Answers
to the nearest whole number.
Answers
I like big black oliy men
How much money should be deposited today in an account that earns 6% compounded monthly so that it will accumulate to $12,000 in three years?
The amount of money that should be deposited is $
Answers
Answer:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount of money accumulated, P is the principal (initial) amount, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
In this problem, we want to find the principal amount P that will accumulate to $12,000 in 3 years at an annual interest rate of 6% compounded monthly. First, we need to convert the annual interest rate to a monthly rate:
r = 0.06/12 = 0.005
Next, we can substitute the given values into the formula and solve for P:
12,000 = P(1 + 0.005/12)^(12*3)
12,000 = P(1.005)^36
P = 12,000/(1.005)^36
P ≈ $9,883.86
Therefore, the amount of money that should be deposited today is approximately $9,883.86.
Step-by-step explanation:
you heard that the Math munch cafe runs a cookie special one a month. For $1.50 you can get 6 cookies at this rate how many cookies could you get for $1.00
Answers
Answer:
4 cookies
Step-by-step explanation:
If you can get 6 cookies for $1.50, then the cost of each cookie is:
$1.50 ÷ 6 = $0.25
This means that for $1.00, you can get:
$1.00 ÷ $0.25 per cookie = 4 cookies
Therefore, you can get 4 cookies for $1.00 at the Math munch cafe.
Which equation can be used to find X
Answers
Answer:
x + 118 = 180
Step-by-step explanation:
Because the angle x added with 118 must be 180 degree for this to be true. So, the answer is x + 118 = 180
Answer:
2.) x + 118 = 180 degrees
Step-by-step explanation:
x + 118 = 180 can be solved as taking 118 on both sides, 118 and 180.
118=0 and 180-118= 62. The other equations in the 4 options do not work.
I hope this helps : )
PLEASE HELP!! I do not understand how to try to solve this!!
Fractions
Barbara, Donna, Cindy and Nicole ran in a relay race. Their times are listed in the chart below
Barbara - 3 3/10
Donna- 2 4/5
Cindy- x
Nicole- 2 1/10
Question- The four girls ran in a relay race as a team. Each girl ran one part of the race. The teams total time was 11 3/5 minutes. What was Cindy's time?
Please help, I can't figure out how to solve this correctly.
Answers
Answer:
Cindy's time was 5 2/5 minutes, or 5.4 minutes to the nearest tenth.
Step-by-step explanation:
To find Cindy's time, we need to use the information given about the total time and the times of the other three runners.
Let's first convert all the times to fractions of a minute:
Barbara: 3 3/10 = 3 + 3/10 = 3.3 minutes
Donna: 2 4/5 = 2 + 4/5 = 2.8 minutes
Cindy: x minutes
Nicole: 2 1/10 = 2 + 1/10 = 2.1 minutes
Now, we can set up an equation to represent the total time of the team:
Barbara's time + Donna's time + Cindy's time + Nicole's time = 11 3/5 minutes
Substituting the values we know:
3.3 + 2.8 + x + 2.1 = 11 3/5
Simplifying and converting mixed numbers to fractions:
8/5 + 14/5 + x + 11/5 = 116/10 + 3/5
Multiplying both sides by 10 to eliminate the denominators:
16 + 28 + 10x + 22 = 116 + 6
Simplifying:
10x = 54
Dividing by 10:
x = 5.4
Therefore, Cindy's time was 5 2/5 minutes, or 5.4 minutes to the nearest tenth.
Can someone help me please? Thank you
Answers
What is the measure of the three missing angles in the rhombus below?
Answers
Answer: see bellow
Step-by-step explanation: Z is 80 Y is 90 and x is 90
This works because each measure is the same arcoss!!!
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Answer:
x = y = 100° z = 80°Step-by-step explanation:
We are interested in finding out the missing angles of the rhombus . Some properties of rhombus that needs to be kept in mind are ,
Opposite angles are equal.All sides are equal.Opposite sides are parallel.[tex]\implies z = 80^o \\[/tex]
[tex]\implies x = y \\[/tex]
Now since the opposite sides are parallel, the sum of co interior angles would be 180° .
Here x and 80° are co interior angles. So their sum would be 180° . Hence,
[tex]\implies x + 80^o = 180^o \\[/tex]
[tex]\implies x = 180^o - 80^o \\[/tex]
[tex]\implies x = 100^o\\[/tex]
Now since x and y were equal , therefore,
[tex]\implies y = 100^o \\[/tex]
Therefore the value of x is 100° , z is 80° and y is 100° .